Shelby County Schools’ mathematics instructional maps are ...



IntroductionIn 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,80% of our students will graduate from high school college or career ready90% of students will graduate on time100% of our students who graduate college or career ready will enroll in a post-secondary opportunityIn order to achieve these ambitious goals, we must collectively work to provide our students with high quality, College and Career Ready standards-aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and Career Ready Standards are rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor. 457200262890000While the academic standards establish desired learning outcomes, the curriculum provides instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational skills are spiraled in order to facilitate student mastery of the standards.These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints () have been designed to show educators a summary of what will be assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail which standards will be assessed on Part I of TNReady and which will be assessed on Part II.4343400274320000Our collective goal is to ensure our students graduate ready for college and career. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation and connections.-571500457200The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations) procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics and sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy). Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.How to Use the Mathematic Curriculum MapsThis curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their instructional practice in alignment with the three College and Career Ready shifts, as described above, in instruction for Mathematics. Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the standards and teaching practices that teachers should consistently access: The TNCore Mathematics StandardsThe Tennessee Mathematics Standards: can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.Mathematical Teaching Practices NCTM – Mathematics Teaching PracticesCurriculum Maps:Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to a learning target in the second column. Each standard is identified as the following: Major Work, Supporting Content or Additional content.In any single grade, students and teachers should spend the majority of their time on the major work of the grade. Consult your enVision Teachers’ Edition (TE) and other cited references to map out your week(s) of instruction.Plan your weekly and daily objectives, using the learning target statements to help. Best practices tell us that making objectives measureable increases student mastery.Include daily fluency practice.Study the suggested performance assessments (tasks) and match them to your objectives.Review the CLIP Connections found in the right hand column. Make plans to address the Academic Vocabulary in your instruction.Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard.Using your enVision TE and other resources cited in the curriculum map, plan your week using the SCS lesson plan template. Remember to include differentiated activities to address the needs of all students.Grade 4: Quarter 2Topic 5: Multiplying by 1-Digit NumbersTopic 7: Multiplying by 2-Digit NumbersTopic 8: Dividing by 1-Digit NumbersTopic 9: Angles (Partial)Topic 14: Perimeter and Area (Partial)Topic 10: Understanding FractionsOverviewStudents move into Topic 5 and learn to round to any place value (4.NBT.A.3), initially using the vertical number line, though ultimately moving away from the number line altogether. This also includes word problems where students apply rounding to real life situations. Students use their place value understanding and understanding of the area model to empower them to multiply by larger numbers. They move to the abstract level by explicitly connecting the partial products appearing in the area model to the distributive property and recording the calculations vertically (4.NBT.B.5). Students use place value to multiply single digit numbers by multiples of ten one hundred and one thousand and two digit multiples of ten by two digit multiples of ten (4.NBT.B.5). As students progress through this topic they are able to apply the multiplication and division algorithms because of their in depth experience with the place value system and multiple conceptual models. Students write equations from statements within the problems (4.OA.A.1) and use a combination of addition, subtraction and multiplication to solve. They must create diagrams to represent these problems as well as write equations with symbols for the unknown quantities (4.OA.A.1). Topic 5 and 7 give students the opportunity to apply their new multiplication skills to solve multi step word problems (4.OA.A.3, 4.NBT.B5) and multiplicative comparison problems (4.OA.A.2). Students focus on interpreting the remainder within division problems in word problems as they transition to Topic 8 (4.OA.A.3) . Students represent division with single digit divisors using arrays and the area model before practicing with place value rods. The standard division algorithm is practiced using place value knowledge decomposing unit by unit. Finally students use the area model to solve division problems first with and then without remainders (4.NBT.B.6). In Topic 8 armed with an understanding of remainders students explore factors, multiples and prime and composite numbers within one hundred (4.OA.B.4) gaining valuable insights into patterns of divisibility as they test for primes and find factors and multiples. This prepares them for future work, working with multi digit dividends. Topic 8 extends the practice of division with three and four digit dividends using place value understandings. A connection is also made initially with dividing multiples of ten one hundred and one thousand by single digit numbers. Place value rods support students visually as they decompose each unit before dividing. Students then practice using a standard algorithm to record long division. They solve word problems and make connections to the area model as was done with two digit dividends (4.NBT.B.6, 4.OA.A.3).In Topic 9 students use dividing the circumference of a circle into 360 equal parts as they recognize one part representing 1 degree (4.MD.C.5a). Students realize that although the size of a circle may change an angle spans an arc representing a constant fraction of a circumference. Armed with their understanding of the degree as a unit of measure, students use various types of protractors to measure angles to the nearest degree and sketch angles of a given measure (4.MD.C.6). The idea that an angle measures the amount of turning in a particular direction is explored as students recognize familiar angles in varied contexts (4.G.A.1, 4.MD.C.5b). In (4.MD.C.7) students solve unknown angle problems. We will briefly visit Topic 14 whereby students use multiplication to solve for area and perimeter. Students must multiply and use formulas to determine the area and perimeter for rectangles in real world and mathematical problems (4.NBT.B.5, 4.MD.A.3). This is an introduction and will be continued in a future quarter.In Topic 10, students begin using multiplication to create an equivalent fraction that comprises smaller units (4.NF.A.1). Based on the use of multiplication, they reason that division can be used to create a fraction that comprises larger units (or single units) equivalent to a given fraction. Students also reason that comparing fractions can only be done when referring to the same whole and they record their comparisons using the comparison symbols <, >, = (4.NF.A.2)(OA.A.2). Students compare fractions greater than one building on their rounding skills and using understanding of benchmarks to reason about which of two fractions is greats (4.NF.A.2)(4.NBT. A.3). This continues to build understanding of the relationship between the numerator and denominator of a fraction. Focus Grade Level StandardsCluster 4.NBT.A Generalize place value understanding for multi-digit whole numbers. 4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place. (2.NBT.A.1, 3.NBT.A.1)Cluster 4.NBT.B Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (3.OA.A.1, 3.OA.B.5, 3.OA.C.7)4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (3.OA.A.2, 3.OA.B.5, 3.OA.C.7)Cluster 4.OA.A Use the four operations with whole numbers to solve problems. 4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. (3.NBT.A.2, 3.OA.A.1, 3.NBT.A.3)4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison. (3.NBT.A.2, 3.OA.A.1, 3.OA.A.2, 3.OA.A.3) 4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (3.NBT.A.2, 3.OA.A.1, 3.OA.D.8)Cluster 4.OA.B Gain familiarity with factors and multiples.4.OA.B.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. (3.OA.A.1, 3.OA.A.2)Cluster 4.G.A Draw and identify lines and angles, and classify shapes by properties of their lines and angles.4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Cluster 4.MD.C Geometric measurement: understand concepts of angle and measure angles.4.MD.C.5.a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. (4.G.A.1)4.MD.C.5.b An angle that turns through n one-degree angles is said to have an angle measure of n degrees. (4.G.A.1)4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. (4.G.A.1, 4.MD.A.5)4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (3.NF.A.3, 4.NBT.A.2)Cluster 4.MD.A Solve problems involving measurement and conversion of measurements.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. (3.MD.C.5, 3.MD.C.6, 3.MD.C.7, 4.NBT.B.5)Cluster 4.NF.A Extend understanding of fraction equivalence and ordering. 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (3.NF.A.1, 3.NF.A.2, 3.NF.A.3) 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (3.NF.A.1, 3.NF.A.2, 3.NF.A.3)Foundational Standards(Note: Related Foundational Standards are noted in parenthesis after standard)?2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the special cases. 3.OA.A.1 Interpret products of whole numbers. 3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.? 3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 3.OA.B.5 Apply properties of operations as strategies to multiply and divide. 3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. 3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100. 3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. 3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is portioned into b equal parts; understand a fraction a/bas the quantity formed by a parts of size 1/b. 3.NF.A.2 Represent a fraction 1/b on a number line diagram. 3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.C.7: Understand concepts of area and relate area to multiplication and to addition. 4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.4.MD.C.5.a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. 4.MD.C.5.b An angle that turns through n one-degree angles is said to have an angle measure of n degrees.02959100Fluency PracticeNCTM PositionProcedural fluency is a critical component of mathematical proficiency. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another. To develop procedural fluency, students need experience in integrating concepts and procedures and building on familiar procedures as they create their own informal strategies and procedures. Students need opportunities to justify both informal strategies and commonly used procedures mathematically, to support and justify their choices of appropriate procedures, and to strengthen their understanding and skill through distributed practice.Fluency is designed to promote automaticity by engaging students in practice in ways that get their adrenaline flowing. Automaticity is critical so that students avoid using up too many of their attention resources with lower-level skills when they are addressing higher-level problems. The automaticity prepares students with the computational foundation to enable deep understanding in flexible ways. Therefore it is recommended that students participate in fluency practice daily. It should be high-paced and energetic, celebrating improvement and focusing on recognizing patterns and connections within the material. Special care should be taken so that it is not seen as punitive for students that might need more time to master fluency.Standards for Mathematical Practice0894080Make sense of problems and persevere in solving them.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others.Model with mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structure.Look for and express regularity in repeated reasoning.00Make sense of problems and persevere in solving them.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others.Model with mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structure.Look for and express regularity in repeated reasoning.4800600665480Resources: : eight Standards for Mathematical Practice are an important component of the mathematics standards for each grade and course, K-12.? The Standards for Mathematical Practice describe the varieties of expertise, habits of minds, and productive dispositions that educators seek to develop in all students.TN State StandardsEssential UnderstandingsContent & TasksCLIP ConnectionsTopic 5: Multiplying by 1-Digit Numbers(Allow 1.5 weeks for instruction, review and assessment)Cluster 4.NBT.A Generalize place value understanding for multi-digit whole numbers. 4.NBT.A.3: Use place value understanding to round multi-digit whole numbers to any place.Cluster 4.NBT.B Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.B.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.Cluster 4.OA.A Use the four operations with whole numbers to solve problems. 4.OA.A.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.4.OA.A.2: Multiply or divide to solve word problems involving multiplicative comparison. 4.OA.A.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.Enduring UnderstandingsThere is more than one way to do a mental calculation. Techniques involve changing the numbers or the expression so the calculation is easy to do mentally.Partial products can be added together to find the product.The standard multiplication algorithm is a short cut for the expanded algorithm. Regrouping is used.The standard algorithm for multiplying a 3-digit number by one digit is just an extension to the hundreds place of the algorithm for multiplying 2-digit by one digit.Different numerical expressions can have the same value.Rounding is one way to estimate products.Basic facts and place value patterns can be used to find products when one factor is 10 or 100.Answers to problems should always be checked for reasonableness by using estimation or checking the answers against the rmation in a problem can be shown using a picture or diagram.Essential QuestionsWhat place-value patterns can be seen when you multiply 1-digit numbers by multiples of 10 and 100?What are some ways to multiply mentally?How can you use rounding to estimate when you multiply?How do you know if your answer is reasonable? How can you use models to help you record multiplication? How do you multiply a 2-digit number by a 1-digit number? How do you multiply a 3-digit number by a 1-digit number? How can you draw a picture and write an equation to solve a problem?Learning TargetsI can explain how to use place value and what digits to look for in order to round a multi-digit number. (4.NBT.A.3)I can use place value of the digit to the right of the place to be rounded to determine whether to round up or round down. (4.NBT.A.3)I can write a multi-digit number rounded to any given place. (4.NBT.A.3)I canI can multiply a multi-digit number by a one-digit whole number. (4.NBT.B.5)I can demonstrate multiplication of two two-digit numbers using rectangular arrays, place value and the area model. (4.NBT.B.5)I can solve multiplication of two-digit numbers using properties of operations and equations. (4.NBT.B.5)I can explain how a multiplication equation can be interpreted as a comparison. (4.OA.A.1)I can write an equation for a situation involving multiplicative comparison. (4.OA.A.1)I can distinguish between multiplicative (as many times as) and additive (more) comparisons. (4.OA.A.2)I can determine when to multiply or divide in word problems. (4.OA.A.2)I can solve a multiplication or division word problems involving multiplicative comparisons using drawings and equations. (4.OA.A.2)I can write an equation using a variable to represent the unknown. (4.OA.A.2)I can choose the correct operation to perform at each step of a multi-step word problem. (4.OA.A.3)I can write equations using a variable to represent the unknown. (4.OA.A.3)I can use mental math or estimation strategies to check if my answer is reasonable. (4.OA.A.3)Fluency Practice DailyMultiplying by 1-Digit Numbers(Lessons 5-1, 5-2 and 5-3 are not current 4th grade standards – please use for Tiered/Enrich instruction as needed)5-4 Problem Solving: Reasonableness 5-5 Using an Expanded Algorithm 5-6/5-6A Multiplication: Multiplying 2-Digit by 1- Digit Numbers 5-7 Multiplication: Multiplying 3-Digit by 1-Digit Numbers 5-8/5-8A Problem Solving: Draw a Picture & Write and EquationenVision Math Transitioning to Common Core, Student Lesson: 5-6A – Connecting the Expanded and Standard Algorithms 5-8A – Multiplying 3- and 4-Digit by 1-Digit Numbers Supplemental Engage NY Activities Multi-Digit Whole Numbers(See Topic C Lessons 7-10 zip file) by 10, 100, and 1,000(See Topic B Lessons 4-6 zip file)Multiplication of up to Four Digits by Single-Digit Numbers(See Topic C Lessons 7-11 zip file)Fluency Resources:(See Grade 4 - Sprints – Grade 4 – Module 1)(Click on resource Building Conceptual Understanding and Fluency Through Games)Academic Vocabularymultiply, compatible numbers, expanded algorithm, partial products, array, factor, reasonableness, rounding, bar diagram (tape diagram)Explain Your ThinkingDo You Understand – (see Guided Practice)Writing to Explain – (problem solving section of each lesson)Task Bank (TNCore 4th Grade Task Arc)Multiplication: Exploration of Multiplicative Comparison and the Link to Division Comprehension & Problem Solving(See TE p 94F for more information)Literature ConnectionsWorldScape Readers All Roads Lead to RomeAdditional Literature“Multiplying Menace” by Pam CalvertTopic 7: Multiplying by 2-Digit Numbers(Allow 1.5 weeks for instruction, review and assessment)Cluster 4.OA.A Use the four operations with whole numbers to solve problems. 4.OA.A.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.Cluster 4.NBT.B Use place value understanding and properties of operations to perform multi-digit arithmetic.4.NBT.B.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.Enduring UnderstandingsBasic facts and place-value patterns can be used to mentally multiply a two digit number by a multiple of 10, 100, or 1,000.Rounding and substituting compatible numbers are two ways to estimate products.The expanded algorithm for multiplying by two digit numbers is just an extension of the expanded algorithm for multiplying one digit numbers.The standard multiplication algorithm is a shortcut for the expanded algorithm. Regrouping is used rather than showing all partial products.Essential QuestionsWhat place-value patterns can be seen when you multiply 2 digit numbers by multiples of 10 and 100?What are some ways to multiply mentally?How can you use rounding to estimate when you multiply?How do you know if your answer is reasonable? How can you use arrays to help you record multiplication? How do you multiply a 2-digit number by a 2-digit number? How do you multiply a 3-digit number by a 2-digit number? How do you solve a two-question problem?Learning TargetsI can choose the correct operation to perform at each step of a multi-step word problem. (4.OA.A.3)I can write equations using a variable to represent the unknown. (4.OA.A.3)I can use mental math or estimation strategies to check if my answer is reasonable. (4.OA.A.3)I can multiply a multi-digit number by a one-digit whole number. (4.NBT.B.5)I can demonstrate multiplication of two two-digit numbers using rectangular arrays, place value and the area model. (4.NBT.B.5)I can solve multiplication of two-digit numbers using properties of operations and equations. (4.NBT.B.5)Fluency Practice DailyMultiplying by 2-Digit Numbers(Lessons 7-1 and 7-2 are not current 4th grade standards – please use for Tiered/Enrich instruction as needed)7-3 Arrays and an Expanded Algorithm 7-4/7-4A Multiplication: Multiplying 2-Digit Numbers by Multiples of 10 7-5 Multiplication: Multiplying 2-Digit by 2-Digit Numbers 7-6 Multiplication: Special Cases 7-7 Two Question Problems enVision Math Transitioning to Common Core, Student Lesson: 7-4A - Arrays and An Expanded Algorithms Supplemental Engage NY Activities Comparison Word Problems (See Topic A Lessons 1-3 zip file)Multiplication Word Problems(See Topic D Lessons 12-13 zip file)Multiplication of Two-Digit by Two-Digit Numbers(See Topic H Lessons 34-38 zip file)Fluency Resources:(See Grade 4 - Sprints – Grade 4 – Module 1) Vocabularystandard algorithm, area modelExplain Your ThinkingDo You Understand – (see guided practice)Writing to Explain – (problems solving section of each lesson)Task BankBuses, Vans and Cars ()Deer in the Park ()Ordering Juice Drinks ()Reading Comprehension & Problem SolvingTeaching Tools Literature ConnectionsWorldScape Readers: “First In Space”Additional LiteratureAmanda Beans Amazing Dream Cindy NeuschwanderTopic 8: Dividing by 1-Digit Divisors(Allow 2 weeks for instruction, review and assessment)Cluster 4.OA.A Use the four operations with whole numbers to solve problems. 4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.Cluster 4.OA.B Gain familiarity with factors and multiples. HYPERLINK "" 4.OA.B.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.Cluster 4.NBT.B Use place value understanding and properties of operations to perform multi-digit arithmetic. HYPERLINK "" 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.Enduring UnderstandingsBasic facts and place value patterns can be used to divide multiples of 10 and 100 by 1-digit numbersThere is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients.The remainder when dividing must be less than the divisor. The nature of the question asked determines how to interpret and use the remainder.The relationship between multiplication and division and estimation can be used to determine the place value of the largest digit in a quotient.Every counting number is divisible by 1 and itself, and some counting numbers are also divisible by other numbers.Some counting numbers have exactly two factors; others have more than two.Essential QuestionsHow can you use place value and patterns to help you divide mentally?When and how do you estimate quotients to solve problems?What does it mean when you divide and some are left over?What do you do when there are not enough hundreds to divide?How can you use multiplication to find all the factors of a number?How can you sort numbers by their factors?What hidden questions lie within a multiple-step problem?Learning TargetsI can choose the correct operation to perform at each step of a multi-step word problem. (4.OA.A.3)I can interpret remainders in word problems. (4.OA.A.3)I can write equations using a variable to represent the unknown. (4.OA.A.3)I can use mental math or estimation strategies to check if my answer is reasonable. (4.OA.A.3)I can list all of the factor pairs for any whole number in the range 1-100. (4.OA.B.4)I can determine multiples of a given whole number 1-100. (4.OA.B.4)I can determine if a number is prime or composite. (4.OA.B.4)I can demonstrate division of a multi-digit number by a one-digit number using place value, rectangular arrays, and area models. (4.NBT.B.6)I can solve division of a multi-digit number by a one-digit number using property of operations and equations. (4.NBT.B.6)I can explain my chosen strategy. (4.NBT.B.6)Fluency Practice DailyDividing by 1-Digit Divisors8-1 Using Mental Math to Divide 8-2 Estimating Quotients 8-3 Dividing with Remainders 8-4 Division: Connecting Models and Symbols 8-5 Dividing 2-Digit by 1-Digit Numbers 8-6 Dividing 3-Digit by 1-Digit Numbers 8-7 Deciding Where to Start Dividing 8-8 Number Sense: Factors 8-9 Prime and Composite Numbers 8-10 Problem Solving: Multiple-Step Problems enVision Math Transitioning to Common Core, Student Lesson: 8-3A Estimating Quotients for Greater Dividends enVision Math Transitioning to Common Core, Student Lesson: 8-4B Using Objects to Divide: Division as Repeated SubtractionenVision Math Transitioning to Common Core, Student Lesson: 8-3C - Division as Repeated Subtraction enVision Math Transitioning to Common Core, Student Lesson: 8-8A Dividing 4-Digit by 1-Digit Numbers Supplemental Engage NY Activities of Tens and Ones with Successive Remainders(See Topic E Lessons 14-21 zip file)Reasoning with Divisibility(See Topic F Lessons 22-25 zip file)Division of Thousands, Hundreds, Tens, and Ones(See Topic G Lessons 26-33 zip file)Fluency Resources:(See Grade 4 - Sprints – Grade 4 – Module 3)(Click on resource Building Conceptual Understanding and Fluency Through Games)Academic Vocabularyremainder, prime number, composite number, factor, multipleExplain Your Thinking Do You Understand – (see guided practice)Writing to Explain – (problems solving section of each lesson)Task Bank (TNCore 4th Grade Task Arc)Multiplication: Exploration of Multiplicative Comparison and the Link to Division Comprehension & Problem SolvingTeaching Tools included with each topicLiterature ConnectionsWorldScape Readers: “All Tied Up”Additional Literature A Remainder of One Elinor PinczesThe Great Divide Dayle Ann DobbsTopic 9: Angles (Includes only content assessed on Part 1 of TN Ready)(Allow 1 week for review and assessment)Cluster 4.G.A Draw and identify lines and angles, and classify shapes by properties of their lines and angles.Cluster 4.MD.C Geometric measurement: understand concepts of angle and measure angles.4.MD.C.5.a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.4.MD.C.5.b An angle that turns through n one-degree angles is said to have an angle measure of n degrees. HYPERLINK "" 4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. HYPERLINK "" 4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.Enduring UnderstandingsMeasurement processes are used in everyday life to describe and quantify the world.Data displays describe and represent data in alternative ways.Essential QuestionsWhy does “what” we measure influence “how” we measure?Why display data in different ways?What is the unit used to measure angles?How are angles measured?How can you add and subtract to find unknown angle measures?Learning TargetsI can identify the parts of an angle (vertex, common endpoint, rays) and define an angle.I can explain that an angle is measured in degrees related to the 360 degrees in a circle.I can explain that the angle measurement of a larger angle is the sum of the angle measures of its decomposed parts.I can write an equation with an unknown angle measurement.I can use addition and subtraction to solve for the missing angle measurements.I can solve word problems involving unknown angles.Fluency Practice DailyLines, Angles and Shapes9-1 Points, Lines, and Planes (4.G.A.1)9-2 Line Segments, Rays, and Angles (4.G.A.1)9-3A Understanding Angles and Unit Angles (4.MD.C.5; 4.MD.C.5a; 4.MD.C.5b; 4.MD.C.6; 4.MD.C.7)9-3B Measuring with Unit Angles (4.G.A.2)9-4A Adding and Subtracting Angle Measures (4.MD.C.5; 4.MD.C.5a; 4.MD.C.5b; 4.MD.C.6; 4.MD.C.7)enVision Math Transitioning to Common Core, Student Lesson: 9-3A Understanding Angles and Unit Angles9-3B Measuring with Unit Angles (4.G.A.2)9-4A Adding and Subtracting Angle MeasuresNote: from TN Ready Final UpdateTeachers should focus on teaching how to find the degree measure of unknown angles in a diagram without a protractor so that students will be prepared for the performance task in February. This requires students to recognize that angles measures are additive. A basic understanding of 4.MD.5 and 4.MD.6 would be helpful to be successful on this task. In addition, students will be required to recognize right angles as stated in 4.G.1.Fluency Resources:(See Grade 4 - Sprints – Grade 4 – Module 1)(Click on resource Building Conceptual Understanding and Fluency Through Games)Academic Vocabularyangle, right angle, acute angle, obtuse angle, straight angle, degree, unit angle, angle measure, protractor, Explain Your Thinking Do You Understand – (see Guided Practice)Writing to Explain – (problem solving section of each lesson)Task Bank Finding an Unknown Angle Comprehension & Problem SolvingTeaching Tool 1Literature ConnectionsWorldScape Readers: “It’s A Big Country”Topic 14: Area & Perimeter (Includes only content assessed on Part 1 of TN Ready) (Allow 2 days for instruction, review and assessment)Cluster 4.MD.A Solve problems involving measurement and conversion of measurements. HYPERLINK "" 4.MD.A.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.Enduring UnderstandingsThe amount of space inside a shape is its area, and area can be estimated or found using square units.The distance around a figure is its perimeter. Formulas exist for finding the perimeter.Essential QuestionsHow do you estimate the area of objects and figures?How do you find the distance around an object?Learning TargetsI can determine the area of a rectangle.I can determine the difference between the length of a rectangle and the perimeter of a rectangle.Fluency Practice DailyArea and Perimeter14-2 Area of Squares and Rectangles (4.MD.A.3)14-6 Perimeter (4.MD.A.3)Note: from TN Ready Final UpdateTeachers should focus on teaching the difference between the length of a rectangle and the perimeter of a rectangle so that students will be prepared for the performance task in February. In addition, the conceptual understanding of how to partition a rectangle into equal areas in conjunction will be helpful in order to complete the performance task. The actual use of the area and perimeter formula is not required for the performance task.Fluency Resources:(See Grade 4 - Sprints – Grade 4 – Module 1)(Click on resource Building Conceptual Understanding and Fluency Through Games)Academic Vocabularyarea, perimeter Explain Your ThinkingDo You Understand – (see Guided Practice)Writing to Explain – (Problem Solving section of each lesson) Reading Comprehension & Problem SolvingTeaching Tool 1Topic 10: Understanding Factions(Allow 2 weeks for instruction, review and assessment)Cluster 4.NF.A Extend understanding of fraction equivalence and ordering. 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.4.OA.A.2: Multiply or divide to solve word problems involving multiplicative comparison. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.Enduring UnderstandingsA fraction describes the division of a whole (region, set, segment) into equal parts. A fraction is relative to the size of the whole.A fraction describes the division of a whole into equal parts, and it can be interpreted in more than one way depending on the whole to be divided.Benchmark fractions can be used to estimate fractional amounts.The same fractional amount can be represented by an infinite set of different but equivalent fractions.A fraction can be expressed in its simplest form by dividing the numerator and denominator by common factors until there are no common factors other than 1.Fractional amounts greater than 1 can be represented using a whole number and a fraction.If two fractions have the same denominator, the fraction with the greater numerator is the greater fraction.Ordering 3 or more numbers is similar to comparing 2 numbers because each number must be compared to each other number.Mathematical explanations can be given using words, pictures, numbers or symbols.Essential QuestionsHow can you show parts of a region?How can you estimate parts?How can you find 2 fractions that name the same part of a whole?How do you write a fraction in simplest form?How can you use benchmark fractions to compare fractions?How do you write a good mathematical explanation?Learning TargetsI can explain why fractions are equivalent using models. (4.NF.A.1)I can generate equivalent fractions by multiplying or dividing the numerator or denominator by the same number. (4.NF.A.1)I can use visual models to justify why multiplying or dividing the numerator and denominator by the same number generates equivalent fractions (4.NF.A.1)I can compare two given fractions by generating equivalent fractions with common denominators. (4.NF.A.2)I can compare two given fractions by reasoning about their size or location on a number line, or comparing them to a benchmark fraction. (4.NF.A.2, OA.A.2)I can record the comparison using symbols (<, >, and =) and justify each comparison. (4.NF.A.2)Fluency Practice DailyUnderstanding Fractions10-2 Fractions and Division 10-3 Fractions: Estimating Fractional Amounts10-4 Fractions: Equivalent Fractions 10-6 Fractions: Improper Fractions and Mixed Numbers 10-7 Fractions: Comparing Fractions 10-8 Fractions: Ordering Fractions 10-9 Problem Solving: Writing to Explain enVision Math Transitioning to Common Core, Student Lesson: 10-5A - Number Lines and Equivalent Fractions Supplemental Engage NY Activities Equivalence Using Multiplication and Division(See Topic B Lessons 7-11 zip file)Fraction Comparison(See Topic C Lessons 12-15 zip file)Extending Fraction Equivalence to Fractions Greater Than 1(See Topic E Lessons 22-28 zip file) Fractions(See Topic A Lessons 1-2 zip file)Fluency Resources:(See Grade 4 - Sprints – Grade 4 – Module 5)(Click on resource Building Conceptual Understanding and Fluency Through Games)Academic Vocabulary fraction, unit fraction, equivalent, multiple, denominator, numerator, benchmark fraction, comparison/compare, improper fraction, simplest form, mixed numberExplain Your ThinkingDo You Understand – (see guided practice)Writing to Explain – (problems solving section of each lesson)Task Bank (TNCore 4th Grade Tasks)Treat BagTwelve CookiesCloser to 1Reading Comprehension & Problem Solving Teaching ToolsLiterature ConnectionsWorldScape Readers: “All Roads Lead to Rome”Additional Literature Apple Fractions Jerry PallottaFraction Action Loreen LeedySkittles Riddles Math Barbara Barbieri McGrathFraction Fun David A. AdlerFractions Are Parts of Things J. Richard DennisRESOURCE TOOLBOXTextbook ResourcesenVision MathenVision Common Core Addendum LessonsCCSS/PARCCTNCore CCSS Toolbox 3PARCCInside MathematicsIllustrative MathematicsEngage NY Math?Additional SitesSCS All Things Mathematics (scsallthingsmath.)Achieve the CoreK-5 Teaching ResourcesSheppard SoftwareBBC BitesizeSingapore MathMath-Play-ComEducation Place?CalculatorTI-15 Interactive ManipulativesRounding?Illuminations?Thinking Blocks Computer and iPad based?PARCC Games?VideosLearnZillionChildren’s LiteratureMultiplying Menace: The Revenge of Rumplestiltskin by Pam CalvertA Remainder of One by Elinor PinczesSafari Park by Stuart J. Murphy (Finding Unknowns)NCTM: Common Core Videos : Videos for the TN State Standards the Core Mini-Assessments the Core: Aligned Instructional Materials ................
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